This invention relates to a method for producing an error signal for the sensing and control of optical interferometers.
Interferometer sensing and control is required for a broad range of scientific and industrial applications. Examples include the frequency stabilisation of diode lasers for fibre optic communication systems, CW wavelength conversion for use in laser printing and photolithographic processes, coherent LIDAR, laser based gyroscope position measuring, remote vibrometry and displacement sensing. The most common approach relies on phase modulation (PM) of the incident laser beam. For multiple beam interferometers, such as the Fabry-Perot interferometer, the Pound-Drever-Hall (PDH) technique is commonly used. This technique has been utilised over the last two decades and when used with high finesse cavities is capable of achieving sub-hertz laser line widths. The PDH modulation frequency is chosen so that the sidebands are non-resonant in the cavity when the carrier field is near resonance. The sidebands are reflected from the cavity with essentially no phase shift The carrier however is near resonance and experiences the full dispersion of the cavity resonance upon reflection. The respective phase shift between the carrier and the sidebands changes the PM symmetry of the incident field introducing some component of amplitude modulation (AM) to the reflected field. As the laser frequency passes through resonance the sign of the AM changes resulting in a zero crossing error signal when the reflected field is detected and demodulated. There are several inherent disadvantages with this PM modulation technique. Firstly the implementation of this technique is complex and expensive. Additionally parasitic AM from the electro-optic modulator can cause significant locking error to occur at time scales of several seconds and longer. The error signal produced at the demodulator output is also typically quite small and consequently the system requires a large gain. Additionally, the small error signal makes the system susceptible to low frequency electronic noise generated within the servo controller for laser frequency.
A prior art approach to laser frequency stabilisation is described in U.S. Pat. No. 4,451,923. The technique described in this patent is based on the interference of polarisation modes. The polarisation interferences are measured by splitting the beam reflected from the cavity through a polarising beam splitter, after passage through some waveplates, and then detecting the respective components of the beam with separate photodetectors. The subtracted outputs from the photodetectors is used to generate an error signal.
U.S. Pat. No. 5,412,676 discloses a method and apparatus for the determination of the relative frequency offset between an input optical signal and a resonance frequency of an optical cavity. The technique described requires a nearly confocal cavity to be used. Additionally, two photodetectors are required each with some form of associated aperture to produce outputs that are subtracted to form an error signal. Another feature of this approach is that the beam transmitted through the cavity is analysed which can result in additional optical phase shift for the error signal in high finesse cavities operating at high frequencies.
Another prior art approach to frequency stabilisation is described by C E Wiemann and S L Gilbert xe2x80x9cLaser frequency stabilisation using mode interference from a reflecting interferometerxe2x80x9d Opt. Lett. Vol. 7, 10, page 480-483, (1982). The technique described in this paper requires the beam reflected from the cavity to be divided by a beam splitter and detected on to photodetectors. One of these detectors has an aperture or diaphragm and the second uses a variable attenuator. This technique can suffer from an intrinsic lack of sensitivity and changes of attenuation or the beam radius may also introduce frequency stabilisation errors.
The present invention proceeds from the recognition that a misaligned mode of an interferometer can be used to act as a phase reference for the correctly aligned fundamental mode of the interferometer. The interference between these two modes is capable of producing an error signal indicative of the phase component the correctly aligned fundamental mode.
In the case of a two beam interferometer, including, but not limited to, a Michelson, Sagnac or Mach-Zehnder interferometer, this error signal is indicative of the phase difference of the two beams, thus allowing the sensing and control of the length difference of the interferometer paths. In the case of a multiple beam interferometer, such as a Fabry-Perot interferometer, this error signal is indicative of the difference between the fundamental mode frequency and the interferometer resonance frequency thus allowing control of the laser frequency with respect to the interferometer resonance frequency.
Accordingly, in one aspect this invention provides a method for sensing and controlling the frequency of a laser with respect to an optical cavity including the steps of introducing a misalignment in the incident laser radiation to the cavity to produce oscillation in the cavity of substantially only a TEM00 mode and a TEM01 mode, and detecting at least two spatially distinct portions of a single beam reflected from the cavity to produce at least two signals each indicative of the respective interference of the two correspondingly spatially distinct portions of the TEM00 mode with two correspondingly spatially distinct portions of the TEM01 mode, and producing an error signal indicative of the difference between the TEM00 mode frequency and the cavity resonance frequency from the signals.
In a second aspect, this invention provides a method for sensing and controlling a two beam interferometer such that the relative path length of the two beams is fixed, including the steps of introducing a misalignment between the two beams to produce substantially only a TEM00 mode and a TEM01 mode, detecting at least two spatially distinct portions of a single beam directed from the interferometer to produce at least two signals each indicative of the interference of the correspondingly spatially distinct portions of the TEM00 mode with the correspondingly spatially distinct portions of the TEM01 mode, and producing an error signal indicative of the path length difference for the TEM00 modes from the signals.
In a third aspect this invention provides an optical system for controlling the frequency of a laser, said system including an optical cavity, means to direct laser radiation into said cavity, means to introduce a misalignment in the incident laser radiation to the cavity to produce oscillation in the cavity of substantially only a TEM00 mode and a TEM01 mode, and means to detect at least two spatially distinct portions of a single beam reflected from the cavity to produce at least two signals each indicative of the respective interference of the two correspondingly spatially distinct portions of the TEM00 mode with two correspondingly spatially distinct portions of the TEM01 mode, and produce an error signal indicative of the difference between the TEM00 mode frequency and the cavity resonance frequency from the signals.
In a fourth aspect this invention provides a two beam interferometer including means to introduce a misalignment between the two beams to produce substantially only a TEM00 mode and a TEM01 mode, means to detect at least two spatially distinct portions of a single beam directed from the interferometer and produce at least two signals each indicative of the interference of the correspondingly spatially distinct portions of the TEM00 mode with the correspondingly spatially distinct portions of the TEM01 mode, and means to produce from said two signals an error signal indicative of the path length difference for the TEM00 modes from the signals.
Preferably, two spatially distinct portions of the beam are detected and they are preferably of equal size. More preferably each form about one half of the cross section of the beam. In the preferred form of the invention the detector is a single entity split into two detecting portions that provide separate outputs.
Preferably the misalignment is generated by tilt or angling the beams. However, it may be more convenient in some interferometer configurations to utilise offset misalignment. Offset misalignment can produce an identical error signal to that produced from tilt misalignment by situating a lens in front of the photodetector. The lens is positioned relative to the detector in such a way that beam offset at the interferometer output is converted into beam tilt at the photodetector.
In the preferred form of the invention the two signals can be directly electronically subtracted to directly provide the error signal.
It will be apparent that the error signal generated in accordance with this invention is used to drive either interferometer control or laser frequency control in the known manner, or as a signal readout of the interferometer.
It will also be apparent that in the case of a multiple beam interferometer in common with the PDH system the method of the present invention utilises a nonresonant field as a phase reference however the field is generated not by modulation but by a simple misalignment of the incident field.
Some embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings.